Principles of Mathematical Analysis by Rudin

[Menomena]

I am curious as to where this book falls in the hierarchy of mathematical education.

Could it be used effectively before a calculus course? Is calculus necessary before analysis?

 

[micromass]

Well, you could use it before a calculus course. But you'll find it much too difficult and without motivation.

To tackle Rudin, one needs to know calculus and one needs to be very familiar with proofs. Furthermore, some mathematical maturity is needed.

And even then, Rudin is still hard.

 

[Menomena]

To tackle Rudin, one needs to know calculus and one needs to be very familiar with proofs. Furthermore, some mathematical maturity is needed.

And even then, Rudin is still hard.

I know its subjective, but what is the definition of "mathematical maturity"?

 

[Number Nine]

I know its subjective, but what is the definition of "mathematical maturity"?

Comfort with abstract mathematical concepts. In general, if you haven't taken calculus yet, then you don't have any (because you've never even encountered abstraction in mathematics). Rudin is something you read after you've already been introduced to real analysis; you are not ready. There are a few good introductory analysis texts (e.g. Elementary Analysis by Ross, which is quite good), but some of the motivation may be lacking if you haven't studied calculus (which isn't to say that you couldn't do it, just that you may not understand the importance of the some of the topics quite yet).

 

[rezeew]

Principles of Mathematical Analysis by Rudin is a highly respected and influential text in the field of mathematical analysis. It is typically used in advanced undergraduate or graduate level courses and assumes a strong foundation in calculus and basic mathematical concepts.

While it is possible to use this book before taking a calculus course, it would be challenging for most students as it builds upon the fundamental concepts and techniques of calculus. It is recommended to have a solid understanding of calculus before delving into analysis.

That being said, some of the material covered in Principles of Mathematical Analysis may overlap with topics covered in a calculus course, so it could potentially be used as a supplement or reference for those studying calculus. However, to fully appreciate and understand the concepts presented in this book, a thorough understanding of calculus is necessary.

In summary, Principles of Mathematical Analysis is a valuable resource for those studying advanced mathematics, but it is best utilized after a solid foundation in calculus has been established.